intersection of two planes

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be perpendicular to both (n_1)^^ and (n_2)^^, which means it is parallel to a = (n_1)^^x(n_2)^^. To uniquely specify the line, it is necessary to also find a particular point on it. This can be determined by finding a point that is simultaneously on both planes, i.e., a point x_0 that satisfies (n_1)^^·x_0 | = | -p_1 (n_2)^^·x_0 | = | -p_2.

bundle of planes | flat | parallel planes | plane | sheaf of planes